In this note, we present some algebraic examples of multicomplexes whose differentials differ from those in the spectral sequences associated to the multicomplexes. The motivation for constructing examples showing the algebraic distinction between a multicomplex and its associated spectral sequence comes from the author's work on Morse-Bott homology with A. Banyaga [A. Banyaga and D. E. Hurtubise, Morse-Bott homology, Trans. Amer. Math. Soc. (to appear), arXiv:math/0612316v2].
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Ajou Univ, Dept Math, San 5,Yeongtong Gu, Woncheon dong 443749, South KoreaAjou Univ, Dept Math, San 5,Yeongtong Gu, Woncheon dong 443749, South Korea
Fu, Xin
Guan, Ai
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Univ Lancaster, Dept Math & Stat, Lancaster LA1 4YF, Lancashire, EnglandAjou Univ, Dept Math, San 5,Yeongtong Gu, Woncheon dong 443749, South Korea
Guan, Ai
Livernet, Muriel
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Univ Paris, Sorbonne Univ, Inst Math Jussieu Paris Gauche R, CNRS, F-75013 Paris, FranceAjou Univ, Dept Math, San 5,Yeongtong Gu, Woncheon dong 443749, South Korea
Livernet, Muriel
Whitehouse, Sarah
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Univ Sheffield, Sch Math & Stat, Sheffield S3 7RH, EnglandAjou Univ, Dept Math, San 5,Yeongtong Gu, Woncheon dong 443749, South Korea